Ultrasonic excitation of a bubble inside a deformable tube: implications for ultrasonically induced hemorrhage

Numerical simulation study on opening blood-brain barrier by ultrasonic cavitation

Experimental studies have shown that ultrasonic cavitation can reversibly open the blood-brain barrier (BBB) to assist drug delivery. Nevertheless, the majority of the present study focused on experimental aspects of BBB opening. In this study, we developed a three-bubble-liquid-solid model to investigate the dynamic behavior of multiple bubbles within the blood vessels, and elucidate the physical mechanism of drug molecules through endothelial cells under ultrasonic cavitation excitation. The results showed that the large bubbles have a significant inhibitory effect on the movement of small bubbles, and the vibration morphology of intravascular microbubbles was affected by the acoustic parameters, microbubble size, and the distance between the microbubbles. The ultrasonic cavitation can significantly enhance the unidirectional flux of drug molecules, and the unidirectional flux growth rate of the wall can reach more than 5 %. Microjets and shock waves emitted from microbubbles generate different stress distribution patterns on the vascular wall, which in turn affects the pore size of the vessel wall and the permeability of drug molecules. The vibration morphology of microbubbles is related to the concentration, arrangement and scale of microbubbles, and the drug permeation impact can be enhanced by optimizing bubble size and acoustic parameters. The results offer an extensive depiction of the factors influencing the blood-brain barrier opening through ultrasonic cavitation, and the model may provide a potential technique to actively regulate the penetration capacity of drugs through endothelial layer of the neurovascular system by regulating BBB opening.

In vivo high-speed microscopy of microbubbles in the chorioallantoic membrane model

Rationale: The acoustic stimulation of microbubbles within microvessels can elicit a spectrum of therapeutically relevant bioeffects from permeabilization to perfusion shutdown. These bioeffects ultimately arise from complex interactions between microbubbles and microvascular walls, though such interactions are poorly understood particularly at high pressure, due to a paucity of direct in vivo observations. The continued development of focused ultrasound methods hinges in large part on establishing links between microbubble-microvessel interactions, cavitation signals, and bioeffects. Methods: Here, a system was developed to enable simultaneous high-speed intravital imaging and cavitation monitoring of microbubbles in vivo in a chorioallantoic membrane model. Exposures were conducted using the clinical agent DefinityTM under conditions previously associated with microvascular damage (1 MHz, 0.5-3.5 MPa, 5 ms pulse length). Results: Ultrasound-activated microbubbles could be observed and were found to induce localized wall deformations that were more pronounced in smaller microvessels and increased with pressure. A central finding was that microbubbles could extravasate from microvessels (from 34% of vessels at 1 MPa to 79% at 3 MPa) during insonation (94% within 0.5 ms) and that this occurred more frequently and in progressively larger microvessels (up to 180 µm) as pressure was increased. Following microbubble extravasation, transient or sustained red blood cell leakage ensued at the extravasation site in 96% of cases for pressures ≥1 MPa. Conclusions: The results here represent the first high-speed in vivo investigation of high-pressure focused ultrasound-induced microbubble-microvessel interactions. This data provides direct evidence that the process of activated microbubble extravasation can occur in vivo and that it is linked to producing microvessel wall perforations of sufficient size to permit red blood cell leakage. The association of red blood cell leakage with microbubble extravasation provides mechanistic insight into the process of microvessel rupture, which has been widely observed in histology.

Experimental study on damage mechanism of blood vessel by cavitation bubbles

Ultrasound-induced cavitation in blood vessels is a common scenario in medical procedures. This paper focuses on understanding the mechanism of microscopic damage to vessel walls caused by the evolution of cavitation bubbles within the vessels. In this study, cavitation bubbles were generated using the low-voltage discharge method in 0.9% sodium chloride saline, and vessel models with wall thicknesses ranging from 0.7 mm to 2 mm were made using a 3D laminating process. The interaction between cavitation bubbles and vessel models with different wall thicknesses was observed using a combination of high-speed photography. Results show that cavitation bubble morphology and collapse time increased and then stabilized as the vessel wall thickness increased. When the cavitation bubble was located in vessel axial line, pair of opposing micro-jets were formed along the axis of the vessel, and the peak of micro-jet velocity decreased with increasing wall thickness. However, when the cavitation bubble deviated from the vessel model center, no micro-jet towards the vessel model wall was observed. Further analysis of the vessel wall deformation under varying distances from the cavitation bubble to the vessel wall revealed that the magnitude of vessel wall stretch due to the cavitation bubble expansion was greater than that of the contraction. A comparative analysis of the interaction of between the cavitation bubble and different forms of elastic membranes showed that the oscillation period of the cavitation bubble under the influence of elastic vessel model was lower than the elastic membrane. Furthermore, the degree of deformation of elastic vessel models under the expansion of the cavitation bubble was smaller than that of elastic membranes, whereas the degree of deformation of elastic vessel models in the contraction phase of the cavitation bubble was larger than that of elastic membranes. These new findings provide important theoretical insights into the microscopic mechanisms of blood vessel potential damage caused by ultrasound-induced cavitation bubble, as well as cavitation in pipelines in hydrodynamic systems.

Prediction of vascular injury by cavitation microbubbles in a focused ultrasound field

Many studies have shown that microbubble cavitation is one mechanism for vascular injury under ultrasonic excitation. Previous work has attributed vascular damage to vessel expansions and invaginations due to the expansion and contraction of microbubbles. However, the mechanisms of vascular damage are not fully understood. In this paper, we investigate, theoretically and experimentally, the vessel injury due to stress induced by ultrasound-induced cavitation (UIC). A bubble-fluid-vessel coupling model is constructed to investigate the interactions of the coupling system. The dynamics process of vessel damage due to UIC is theoretically simulated with a finite element method, and a focused ultrasound (FU) setup is carried out and used to assess the vessel damage. The results show that shear stress contributes to vessel injury by cell detachment while normal stress mainly causes distention injury. Similar changes in cell detachment in a vessel over time can be observed with the experimental setup. The severity of vascular injury is correlated to acoustic parameters, bubble-wall distance, and microbubble sizes, and the duration of insonation..

A 3D finite element model to study the cavitation induced stresses on blood-vessel wall during the ultrasound-only phase of photo-mediated ultrasound therapy

Photo-mediated ultrasound therapy (PUT) is a novel technique utilizing synchronized ultrasound and laser to generate enhanced cavitation inside blood vessels. The enhanced cavitation inside blood vessels induces bio-effects, which can result in the removal of micro-vessels and the reduction in local blood perfusion. These bio-effects have the potential to treat neovascularization diseases in the eye, such as age-related macular degeneration and diabetic retinopathy. Currently, PUT is in the preclinical stage, and various PUT studies on in vivo rabbit eye models have shown successful removal of micro-vessels. PUT is completely non-invasive and particle-free as opposed to current clinical treatments such as anti-vascular endothelial growth factor therapy and photodynamic therapy, and it precisely removes micro-vessels without damaging the surrounding tissue, unlike laser photocoagulation therapy. The stresses produced by oscillating bubbles during PUT are responsible for the induced bio-effects in blood vessels. In our previous work, stresses induced during the first phase of PUT due to combined ultrasound and laser irradiation were studied using a 2D model. In this work, stresses induced during the third or last phase of PUT due to ultrasound alone were studied using a 3D finite element method-based numerical model. The results showed that the circumferential and shear stress increased as the bubble moves from the center of the vessel toward the vessel wall with more than a 16 times increase in shear stress from 1.848 to 31.060 kPa as compared to only a 4 times increase in circumferential stress from 211 to 906 kPa for a 2 µm bubble placed inside a 10 µm vessel on the application of 1 MHz ultrasound frequency and 130 kPa amplitude. In addition, the stresses decreased as the bubble was placed in smaller sized vessels with a larger decrease in circumferential stress. The changes in shear stress were found to be more dependent on the bubble-vessel wall distance, and the changes in circumferential stress were more dependent on the bubble oscillation amplitude. Moreover, the bubble shape changed to an ellipsoidal with a higher oscillation amplitude in the vessel's axial direction as it was moved closer to the vessel wall, and the bubble oscillation amplitude decreased drastically as it was placed in vessels of a smaller size.

Pulsating Microbubble in a Micro-vessel and Mechanical Effect on Vessel Wall: A Simulation Study

Background:

Microbubbles are widely used in diagnostic ultrasound applications as contrast agents. Recently, many studies have shown that microbubbles have good potential for the use in therapeutic applications such as drug and gene delivery and opening of blood- brain barrier locally and transiently. When microbubbles are located inside an elastic microvessel and activated by ultrasound, they oscillate and induce mechanical stresses on the vessel wall. However, the mechanical stresses have beneficial therapeutic effects, they may induce vessel damage if they are too high. Microstreaming-induced shear stress is one of the most important wall stresses.

Objective:

The overall aim of this study is to simulate the interaction between confined bubble inside an elastic microvessel and ultrasound field and investigate the effective parameters on microstreaming-induced shear stress.

Material and Methods:

In this Simulation study, we conducted a 2D finite element simulation to study confined microbubble dynamics, also we investigated both acoustical and bubble material parameters on microbubble oscillation and wall stress.

Results:

Based on our results, for acoustic parameters in the range of therapeutic applications, the maximum shear stress was lower than 4 kPa. Shear stress was approximately independent from shell viscosity whereas it decreased by increasing the shell stiffness. Moreover, shear stress showed an increasing trend with acoustic pressure.

Conclusion:

Beside the acoustical parameters, bubble properties have important effects on bubble behavior so that the softer and larger bubbles are more appropriate for therapeutic application as they can decrease the required frequency and acoustic pressure while inducing the same biological effects.

Opening doors with ultrasound and microbubbles: Beating biological barriers to promote drug delivery

Apart from its clinical use in imaging, ultrasound has been thoroughly investigated as a tool to enhance drug delivery in a wide variety of applications. Therapeutic ultrasound, as such or combined with cavitating nuclei or microbubbles, has been explored to cross or permeabilize different biological barriers. This ability to access otherwise impermeable tissues in the body makes the combination of ultrasound and therapeutics very appealing to enhance drug delivery in situ. This review gives an overview of the most important biological barriers that can be tackled using ultrasound and aims to provide insight on how ultrasound has shown to improve accessibility as well as the biggest hurdles. In addition, we discuss the clinical applicability of therapeutic ultrasound with respect to the main challenges that must be addressed to enable the further progression of therapeutic ultrasound towards an effective, safe and easy-to-use treatment tailored for drug delivery in patients.

The penetration effect of HMME-mediated low-frequency and low-intensity ultrasound against the Staphylococcus aureus bacterial biofilm

Background

The purpose of this study was to observe the effect of hematoporphyrin monomethyl ether (HMME)-mediated low-frequency and low-intensity ultrasound on mature and stable Staphylococcus aureus (S. aureus) biofilms under different ultrasound parameters.

Methods

The biofilm was formed after 48-h culture with stable concentration of bacterial solution. Different types of ultrasound and time were applied to the biofilm, and the ultrasonic type and time of our experiments were determined when the biofilm was not damaged. The penetration effects of low-frequency and low-intensity ultrasound were decided by the amount of HMME that penetrated into the biofilm which was determined by fluorescence spectrometry.

Results

The destruction of biofilms by pulse waveform was the strongest. Sinusoidal low-frequency and low-intensity ultrasound can enhance the biofilm permeability. For a period of time after the ultrasound was applied, the biofilm permeability increased, however, changes faded away over time.

Conclusions

Low-frequency and low-intensity sinusoidal ultrasound significantly increased the permeability of the biofilms, which was positively correlated with the time and the intensity of ultrasound. Simultaneous action of ultrasound and HMME was the most effective way to increase the permeability of the biofilms.

Engineered 3D Microvascular Networks for the Study of Ultrasound-Microbubble-Mediated Drug Delivery

Localized and targeted drug delivery can be achieved by the combined action of ultrasound and microbubbles on the tumor microenvironment, likely through sonoporation and other therapeutic mechanisms that are not well understood. Here, we present a perfusable in vitro model with a realistic 3D geometry to study the interactions between microbubbles and the vascular endothelium in the presence of ultrasound. Specifically, a three-dimensional, endothelial-cell-seeded in vitro microvascular model was perfused with cell culture medium and microbubbles while being sonicated by a single-element 1 MHz focused transducer. This setup mimics the in vivo scenario in which ultrasound induces a therapeutic effect in the tumor vasculature in the presence of flow. Fluorescence and bright-field microscopy were employed to assess the microbubble-vessel interactions and the extent of drug delivery and cell death both in real time during treatment as well as after treatment. Propidium iodide was used as the model drug while calcein AM was used to evaluate cell viability. There were two acoustic parameter sets chosen for this work: (1) acoustic pressure: 1.4 MPa, pulse length: 500 cycles, duty cycle: 5% and (2) acoustic pressure: 0.4 MPa, pulse length: 1000 cycles, duty cycle: 20%. Enhanced drug delivery and cell death were observed in both cases while the higher pressure setting had a more pronounced effect. By introducing physiological flow to the in vitro microvascular model and examining the PECAM-1 expression of the endothelial cells within it, we demonstrated that our model is a good mimic of the in vivo vasculature and is therefore a viable platform to provide mechanistic insights into ultrasound-mediated drug delivery.

The enhanced HIFU-induced thermal effect via magnetic ultrasound contrast agent microbubbles

High intensity focused ultrasound (HIFU) has been regarded as a promising technology for treating cancer and other severe diseases noninvasively. In the present study, dual modality magnetic ultrasound contrast agent microbubbles (MBs) were synthesized by loading the super paramagnetic iron oxide nanoparticles (SPIOs) into the albumin-shelled MBs (referred as SPIO-albumin MBs). Then, both experimental measurements and numerical simulations were performed to evaluate the ability of SPIO-albumin MBs of enhancing HIFU-induced thermal effect. The results indicated that, comparing with regular albumin-shelled MBs, the SPIO-albumin MBs would lead to quicker temperature elevation rate and higher peak temperature. This phenomenon could be explained by the changes in MBs' physical and thermal properties induced by the integration of SPIOs into MB shell materials. In addition, more experimental results demonstrated that the enhancement effect on HIFU-induced temperature elevation could be further strengthened with more SPIOs combined with albumin-shell MBs. These observations suggested that more violent cavitation behaviors might be activated by ultrasound exposures with the presence of SPIOs, which in turn amplified ultrasound-stimulated thermal effect. Based on the present studies, it is reasonable to expect that, with the help of properly designed dual-modality magnetic MBs, the efficiency of HIFU-induced thermal effect could be further improved to achieve better therapeutic outcomes.

Inverse effects of flowing phase-shift nanodroplets and lipid-shelled microbubbles on subsequent cavitation during focused ultrasound exposures

This paper compared the effects of flowing phase-shift nanodroplets (NDs) and lipid-shelled microbubbles (MBs) on subsequent cavitation during focused ultrasound (FUS) exposures. The cavitation activity was monitored using a passive cavitation detection method as solutions of either phase-shift NDs or lipid-shelled MBs flowed at varying velocities through a 5-mm diameter wall-less vessel in a transparent tissue-mimicking phantom when exposed to FUS. The intensity of cavitation for the phase-shift NDs showed an upward trend with time and cavitation for the lipid-shelled MBs grew to a maximum at the outset of the FUS exposure followed by a trend of decreases when they were static in the vessel. Meanwhile, the increase of cavitation for the phase-shift NDs and decrease of cavitation for the lipid-shelled MBs had slowed down when they flowed through the vessel. During two discrete identical FUS exposures, while the normalized inertial cavitation dose (ICD) value for the lipid-shelled MB solution was higher than that for the saline in the first exposure (p-value <0.05), it decreased to almost the same level in the second exposure. For the phase-shift NDs, the normalized ICD was 0.71 in the first exposure and increased to 0.97 in the second exposure. At a low acoustic power, the normalized ICD values for the lipid-shelled MBs tended to increase with increasing velocities from 5 to 30cm/s (r>0.95). Meanwhile, the normalized ICD value for the phase-shift NDs was 0.182 at a flow velocity of 5cm/s and increased to 0.188 at a flow velocity of 15cm/s. As the flow velocity increased to 20cm/s, the normalized ICD was 0.185 and decreased to 0.178 at a flow velocity of 30cm/s. At high acoustic power, the normalized ICD values for both the lipid-shelled MBs and the phase-shift NDs increased with increasing flow velocities from 5 to 30cm/s (r>0.95). The effects of the flowing phase-shift NDs vaporized into gas bubbles as cavitation nuclei on the subsequent cavitation were inverse to those of the flowing lipid-shelled MBs destroyed after focused ultrasound exposures.

The breakup of intravascular microbubbles and its impact on the endothelium

Encapsulated microbubbles (MBs) serve as endovascular agents in a wide range of medical ultrasound applications. The oscillatory response of these agents to ultrasonic excitation is determined by MB size, gas content, viscoelastic shell properties and geometrical constraints. The viscoelastic parameters of the MB capsule vary during an oscillation cycle and change irreversibly upon shell rupture. The latter results in marked stress changes on the endothelium of capillary blood vessels due to altered MB dynamics. Mechanical effects on microvessels are crucial for safety and efficacy in applications such as focused ultrasound-mediated blood-brain barrier (BBB) opening. Since direct in vivo quantification of vascular stresses is currently not achievable, computational modelling has established itself as an alternative. We have developed a novel computational framework combining fluid-structure coupling and interface tracking to model the nonlinear dynamics of an encapsulated MB in constrained environments. This framework is used to investigate the mechanical stresses at the endothelium resulting from MB shell rupture in three microvessel setups of increasing levels of geometric detail. All configurations predict substantial elevation of up to 150 % for peak wall shear stress upon MB breakup, whereas global peak transmural pressure levels remain unaltered. The presence of red blood cells causes confinement of pressure and shear gradients to the proximity of the MB, and the introduction of endothelial texture creates local modulations of shear stress levels. With regard to safety assessments, the mechanical impact of MB breakup is shown to be more important than taking into account individual red blood cells and endothelial texture. The latter two may prove to be relevant to the actual, complex process of BBB opening induced by MB oscillations.

A Two-Criterion Model for Microvascular Bio-Effects Induced In Vivo by Contrast Microbubbles Exposed to Medical Ultrasound

The mechanical index (MI) is a theoretical exposure parameter for cavitational bio-effects of diagnostic ultrasound. The theory for the MI assumed that bubbles of all relevant sizes exist in tissue, a condition that is approximated for tissues that include a microbubble contrast agent. Therefore, the MI should allow science-based safety guidance for contrast-enhanced diagnostic ultrasound. However, theoretical predictions of bio-effects thresholds based on the MI typically do not concur with the frequency dependence of experimentally measured thresholds for bio-effects. For example, experimental thresholds for glomerular capillary hemorrhage in rats infused with contrast microbubbles increased approximately linearly with frequency, whereas the MI predicted a square root dependence. Here, cavitation thresholds were computed for linear versions of the acoustic pulses used in that study assuming bubbles containing either air, C3F8, or a 1:1 mixture of the two and surrounded by either blood or kidney tissue. Although no single threshold criterion was successful, combining results for one criterion that maximized circumferential stress in the capillary wall with another that ensured an inertial collapse produced thresholds that were consistent with experimental data. This suggests that a contrast-specific safety metric may be achieved following validation of this two-criterion model.

Breast tumor response to ultrasound mediated excitation of microbubbles and radiation therapy in vivo

Acoustically stimulated microbubbles have been demonstrated to perturb endothelial cells of the vasculature resulting in biological effects. In the present study, vascular and tumor response to ultrasound-stimulated microbubble and radiation treatment was investigated in vivo to identify effects on the blood vessel endothelium. Mice bearing breast cancer tumors (MDA-MB-231) were exposed to ultrasound after intravenous injection of microbubbles at different concentrations, and radiation at different doses (0, 2, and 8 Gy). Mice were sacrificed 12 and 24 hours after treatment for histopathological analysis. Tumor growth delay was assessed for up to 28 days after treatment. The results demonstrated additive antitumor and antivascular effects when ultrasound stimulated microbubbles were combined with radiation. Results indicated tumor cell apoptosis, vascular leakage, a decrease in tumor vasculature, a delay in tumor growth and an overall tumor disruption. When coupled with radiation, ultrasound-stimulated microbubbles elicited synergistic anti-tumor and antivascular effects by acting as a radioenhancing agent in breast tumor blood vessels. The present study demonstrates ultrasound driven microbubbles as a novel form of targeted antiangiogenic therapy in a breast cancer xenograft model that can potentiate additive effects to radiation in vivo.

Microbubble oscillating in a microvessel filled with viscous fluid: A finite element modeling study

Understanding the dynamics of coated-microbubble oscillating in an elastic microvessel is important for effective and safe applications of ultrasound contrast agents (UCAs) in imaging and therapy. Numerical simulations are performed based on a two-dimensional (2D) asymmetric finite element model to investigate the influences of both acoustic driving parameters (e.g., pressure and frequency) and material properties (vessel size, microbubble shell visco-elastic parameters and fluid viscosity) on the dynamic interactions in the bubble-blood-vessel system. The results show that, the constrained effect of the blood vessel along the radial direction will induce the asymmetric bubble oscillation and vessel deformation, as well as shifting the bubble resonance frequency toward the higher frequency range. For a bubble (1.5-μm radius) activated by 1-MHz ultrasound pulses in a microvessel with a radius varying between 2 and 6.5 μm, up to 26.95 kPa shear stress could be generated on the vessel wall at a driving pressure of 0.2 MPa, which should be high enough to damage the vascular endothelial cells. The asymmetrical oscillation ratio of the bubble can be aggravated from 0.12% to 79.94% with the increasing acoustic driving pressure and blood viscosity, or the decreasing vessel size and microbubble shell visco-elastic properties. The maximum compression velocity on the bubble shell will be enhanced from 0.19 to 22.79 m/s by the increasing vessel size and acoustic pressure, or the decreasing microbubble shell visco-elasticity and blood viscosity. As the results, the peak values of microstreaming-induced shear stress on the vessel wall increases from 0.003 to 26.95 kPa and the deformation degree of vessel is raised from 1.01 to 1.49, due to the enhanced acoustic amplitude, or the decreasing vessel size, blood viscosity and microbubble shell visco-elasticity. Moreover, it also suggests that, among above impact parameters, microbubble resonance frequency and UCA shell elasticity might play more dominant roles in dynamic interactions of the bubble-blood-vessel system.

Theoretical study of microbubble dynamics in sonoporation

Sonoporation is a promising technology for promoting the transfer of drug or gene into cells using ultrasound-mediated microbubbles that transiently break up the cell membrane. In this article, a model is established to analyze the dynamics of ultrasound-mediated microbubble near the cell membrane, which may be especially useful for understanding the mechanisms of sonoporation. In the model, the velocity potential of fluid on the microbubble surface and on the cell membrane is obtained by the unsteady Bernoulli equations, and it is solved by using the boundary integral equations. By numerically analyzing the model, the typical microbubble dynamics near the cell membrane are enumerated, which may be mainly governed by mechanical index. The model also established the connections among the parameters of ultrasound exposure, microbubble characteristics, and cell membrane properties in sonoporation.

Microbial biofilm modulation by ultrasound: current concepts and controversies

Biofilm elimination is often necessary during antimicrobial therapy or industrial medical manufacturing decontamination. In this context, ultrasound treatment has been frequently described in the literature for its antibiofilm effectiveness, but at the same time, various authors have described ultrasound as a formidable enhancer of bacterial viability. This discrepancy has found no solution in the current literature for around 9 years; some works have shown that every time bacteria are exposed to an ultrasonic field, both destruction and stimulation phenomena co-exist. This co-existence proves to have different final effects based on various factors such as: ultrasound frequency and intensity, the bacterial species involved, the material used for ultrasound diffusion, the presence of cavitation effects and the forms of bacterial planktonic or biofilm. The aim of this work is to analyze current concepts regarding ultrasound effect on prokaryotic cells, and in particular ultrasound activity on bacterial biofilm.

Mechanisms of microbubble-vessel interactions and induced stresses: a numerical study

Oscillating microbubbles within microvessels could induce stresses that lead to bioeffects or vascular damage. Previous work has attributed vascular damage to the vessel expansion or bubble jet. However, ultra-high speed images of recent studies suggest that it could happen due to the vascular invagination. Numerical simulations of confined bubbles could provide insight into understanding the mechanism behind bubble-vessel interactions. In this study, a finite element model of a coupled bubble/fluid/vessel system was developed and validated with experimental data. Also, for a more realistic study viscoelastic properties of microvessels were assessed and incorporated into this comprehensive numerical model. The wall shear stress (WSS) and circumferential stress (CS), metrics of vascular damage, were calculated from these simulations. Resultant amplitudes of oscillation were within 15% of those measured in experiments (four cases). Among the experimental cases, it was numerically found that maximum WSS values were between 1.1-18.3 kPa during bubble expansion and 1.5-74 kPa during bubble collapse. CS was between 0.43-2.2 MPa during expansion and 0.44-6 MPa while invaginated. This finding confirmed that vascular damage could occur during vascular invaginations. Predicted thresholds in which these stresses are higher during vessel invagination were calculated from simulations.

Shock-induced collapse of a bubble inside a deformable vessel

Shockwave lithotripsy repeatedly focuses shockwaves on kidney stones to induce their fracture, partially through cavitation erosion. A typical side effect of the procedure is hemorrhage, which is potentially the result of the growth and collapse of bubbles inside blood vessels. To identify the mechanisms by which shock-induced collapse could lead to the onset of injury, we study an idealized problem involving a preexisting bubble in a deformable vessel. We utilize a high-order accurate, shock- and interface-capturing, finite-volume scheme and simulate the three-dimensional shock-induced collapse of an air bubble immersed in a cylindrical water column which is embedded in a gelatin/water mixture. The mixture is a soft tissue simulant, 10% gelatin by weight, and is modeled by the stiffened gas equation of state. The bubble dynamics of this model configuration are characterized by the collapse of the bubble and its subsequent jetting in the direction of the propagation of the shockwave. The vessel wall, which is defined by the material interface between the water and gelatin/water mixture, is invaginated by the collapse and distended by the impact of the jet. The present results show that the highest measured pressures and deformations occur when the volumetric confinement of the bubble is strongest, the bubble is nearest the vessel wall and/or the angle of incidence of the shockwave reduces the distance between the jet tip and the nearest vessel surface. For a particular case considered, the 40 MPa shockwave utilized in this study to collapse the bubble generated a vessel wall pressure of almost 450 MPa and produced both an invagination and distention of nearly 50% of the initial vessel radius on a 𝒪(10) ns timescale. These results are indicative of the significant potential of shock-induced collapse to contribute to the injury of blood vessels in shockwave lithotripsy.

Modelling single- and tandem-bubble dynamics between two parallel plates for biomedical applications

Carefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.

Dynamics of micro-bubble sonication inside a phantom vessel

A model for sonicated micro-bubble oscillations inside a phantom vessel is proposed. The model is not a variant of conventional Rayleigh-Plesset equation and is obtained from reduced Navier-Stokes equations. The model relates the micro-bubble oscillation dynamics with geometric and acoustic parameters in a consistent manner. It predicts micro-bubble oscillation dynamics as well as micro-bubble fragmentation when compared to the experimental data. For large micro-bubble radius to vessel diameter ratios, predictions are damped, suggesting breakdown of inherent modeling assumptions for these cases. Micro-bubble response with acoustic parameters is consistent with experiments and provides physical insight to the micro-bubble oscillation dynamics.

Characteristic microvessel relaxation timescales associated with ultrasound-activated microbubbles

Ultrasound-activated microbubbles were used as actuators to deform microvessels for quantifying microvessel relaxation timescales at megahertz frequencies. Venules containing ultrasound contrast microbubbles were insonified by short 1 MHz ultrasound pulses. Vessel wall forced-deformations were on the same microsecond timescale as microbubble oscillations. The subsequent relaxation of the vessel was recorded by high-speed photomicrography. The tissue was modeled as a simple Voigt solid. Relaxation time constants were measured to be on the order of ∼10 μs. The correlation coefficients between the model and 38 data sets were never lower than 0.85, suggesting this model is sufficient for modeling tissue relaxation at these frequencies. The results place a bound on potential numerical values for viscosity and elasticity of venules.

Model for bubble pulsation in liquid between parallel viscoelastic layers

A model is presented for a pulsating spherical bubble positioned at a fixed location in a viscous, compressible liquid between parallel viscoelastic layers of finite thickness. The Green's function for particle displacement is found and utilized to derive an expression for the radiation load imposed on the bubble by the layers. Although the radiation load is derived for linear harmonic motion it may be incorporated into an equation for the nonlinear radial dynamics of the bubble. This expression is valid if the strain magnitudes in the viscoelastic layer remain small. Dependence of bubble pulsation on the viscoelastic and geometric parameters of the layers is demonstrated through numerical simulations.

Compare ultrasound-mediated heating and cavitation between flowing polymer- and lipid-shelled microbubbles during focused ultrasound exposures

This paper compares the efficiency of flowing polymer- and lipid-shelled microbubbles (MBs) in the heating and cavitation during focused ultrasound exposures. Temperature and cavitation activity were simultaneously measured as the two types of shelled MBs and saline flowing through a 3 mm diameter vessel in the phantom with varying flow velocities (0-20 cm/s) at different acoustic power levels (0.6-20 W) with each exposure for 5 s. Temperature and cavitation for the lipid-shelled MBs were higher than those for the polymer-shelled MBs. Temperature rise decreased with increasing flow velocities for the two types of shelled MBs and saline at acoustic power 1.5 W. At acoustic power 11.1 W, temperature rise increased with increasing flow velocities for the lipid-shelled MBs. For the polymer-shelled MBs, the temperature rise increased with increasing flow velocities from 3-15 cm/s and decreased at 20 cm/s. Cavitation increased with increasing flow velocity for the two shelled MBs and there were no significant changes of cavitation with increasing flow velocities for saline. These results suggested that lipid-shelled MBs may have a greater efficiency than polymer-shelled MBs in heating and cavitation during focused ultrasound exposures.

MODELING MICROBUBBLE DYNAMICS IN BIOMEDICAL APPLICATIONS()

Controlling microbubble dynamics to produce desirable biomedical outcomes when and where necessary and avoid deleterious effects requires advanced knowledge, which can be achieved only through a combination of experimental and numerical/analytical techniques. The present communication presents a multi-physics approach to study the dynamics combining viscous- in-viscid effects, liquid and structure dynamics, and multi bubble interaction. While complex numerical tools are developed and used, the study aims at identifying the key parameters influencing the dynamics, which need to be included in simpler models.

A three-dimensional model of an ultrasound contrast agent gas bubble and its mechanical effects on microvessels

Ultrasound contrast agents inside a microvessel, when driven by ultrasound, oscillate and induce mechanical stresses on the vessel wall. These mechanical stresses can produce beneficial therapeutic effects but also induce vessel rupture if the stresses are too high. Therefore, it is important to use sufficiently low pressure amplitudes to avoid rupturing the vessels while still inducing the desired therapeutic effects. In this work, we developed a comprehensive three-dimensional model of a confined microbubble inside a vessel while considering the bubble shell properties, blood viscosity, vessel wall curvature and the mechanical properties of the vessel wall. Two bubble models with the assumption of a spherical symmetric bubble and a simple asymmetrical bubble were simulated. This work was validated with previous experimental results and enabled us to evaluate the microbubbles' behaviour and the resulting mechanical stresses induced on the vessel walls. In this study, the fluid shear and circumferential stresses were evaluated as indicators of the mechanical stresses. The effects of acoustical parameters, vessel viscoelasticity and rigidity, vessel/bubble size and off-centre bubbles on bubble behaviour and stresses on the vessel were investigated. The fluid shear and circumferential stresses acting on the vessel varied with time and location. As the frequency changed, the microbubble oscillated with the highest amplitude at its resonance frequency which was different from the resonance frequency of an unbound bubble. The bubble resonance frequency increased as the rigidity of a flexible vessel increased. The fluid shear and circumferential stresses peaked at frequencies above the bubble's resonance frequency. The more rigid the vessels were, the more damped the bubble oscillations. The synergistic effect of acoustic frequency and vessel elasticity had also been investigated since the circumferential stress showed either an increasing trend or a decreasing one versus the vessel rigidity at different acoustic frequencies. When the acoustic pressure was increased from 52 to 680 kPa, the maximum bubble radius increase by 2.5 fold, and the maximum shear and circumferential stress increased by 15.7 and 18.3 fold, respectively. The shear stress was largest when the acoustic frequency was higher (3.25 MHz) and the ratio of the vessel radius to the bubble radius was lower. The circumferential stress was largest when the bubble wall was closer to the vessel wall. An oscillating off-centre bubble forms a mushroom shape with the most damping on the points closest to the vessel wall.

Natural frequencies of two bubbles in a compliant tube: analytical, simulation, and experimental results

Motivated by various clinical applications of ultrasound contrast agents within blood vessels, the natural frequencies of two bubbles in a compliant tube are studied analytically, numerically, and experimentally. A lumped parameter model for a five degree of freedom system was developed, accounting for the compliance of the tube and coupled response of the two bubbles. The results were compared to those produced by two different simulation methods: (1) an axisymmetric coupled boundary element and finite element code previously used to investigate the response of a single bubble in a compliant tube and (2) finite element models developed in comsol Multiphysics. For the simplified case of two bubbles in a rigid tube, the lumped parameter model predicts two frequencies for in- and out-of-phase oscillations, in good agreement with both numerical simulation and experimental results. For two bubbles in a compliant tube, the lumped parameter model predicts four nonzero frequencies, each asymptotically converging to expected values in the rigid and compliant limits of the tube material.

A reduced-order, single-bubble cavitation model with applications to therapeutic ultrasound

Cavitation often occurs in therapeutic applications of medical ultrasound such as shock-wave lithotripsy (SWL) and high-intensity focused ultrasound (HIFU). Because cavitation bubbles can affect an intended treatment, it is important to understand the dynamics of bubbles in this context. The relevant context includes very high acoustic pressures and frequencies as well as elevated temperatures. Relative to much of the prior research on cavitation and bubble dynamics, such conditions are unique. To address the relevant physics, a reduced-order model of a single, spherical bubble is proposed that incorporates phase change at the liquid-gas interface as well as heat and mass transport in both phases. Based on the energy lost during the inertial collapse and rebound of a millimeter-sized bubble, experimental observations were used to tune and test model predictions. In addition, benchmarks from the published literature were used to assess various aspects of model performance. Benchmark comparisons demonstrate that the model captures the basic physics of phase change and diffusive transport, while it is quantitatively sensitive to specific model assumptions and implementation details. Given its performance and numerical stability, the model can be used to explore bubble behaviors across a broad parameter space relevant to therapeutic ultrasound.

The inertial terms in equations of motion for bubbles in tubular vessels or between plates

Equations resembling the Rayleigh-Plesset and Keller-Miksis equations are frequently used to model bubble dynamics in confined spaces, using the standard inertial term RR+3R([middle dot]) (2)/2, where R is the bubble radius. This practice has been widely assumed to be defensible if the bubble is much smaller than the radius of the confining vessel. This paper questions this assumption, and provides a simple rigid wall model for worst-case quantification of the effect on the inertial term of the specific confinement geometry. The relevance to a range of scenarios (including bubbles confined in microfluidic devices; or contained in test chambers for insonification or imaging; or in blood vessels) is discussed.

Forced vibrations of a bubble in a liquid-filled elastic vessel

There is increasing demand for accurate characterization of the in vivo behavior of microbubble agents used for ultrasound imaging and therapy. This study examines bubble-vessel interaction, in particular the propagation of disturbances along the vessel wall. Finite element simulations of a 3 μm radius microbubble suspended in a viscous liquid and enclosed in a 4 μm radius elastic vessel were performed, and the results compared with existing analytical results for wave propagation in elastic liquid-filled tubes. The vessel wall was shown to have a significant effect upon the amplitude of bubble oscillation and hence acoustic radiation from it, as well as distension of the vessel wall. It was found that the most important factor was the ratio of the excitation frequency to the natural "ring" frequency of the vessel which in turn depends upon its dimensions and mechanical properties. As this ratio increases, the motion of the vessel wall becomes increasingly localized to the site of the bubble. It was also shown that the validity of the results obtained using the applied model of vessel elasticity is limited to frequencies below the ring frequency, and this should be taken into account in the development of protocols for ultrasound safety and/or therapeutic procedures.

Minimizing the thermal losses from perfusion during focused ultrasound exposures with flowing microbubbles

This paper demonstrated the use of flowing microbubbles (MBs) to minimize thermal losses from perfusion during focused ultrasound exposures due to acoustic cavitation. Temperature and cavitation were simultaneously investigated as MBs flowing through a wall-less flow phantom with varying flow velocities (2-55 cm/s) and concentrations (0%-0.1%) when exposed at different acoustic power levels (5-120 W). The peak temperature at the end of ultrasonic exposures in the flow and in the outer of the vessel as well as the cavitation were higher than those pure controls measured at the same exposure parameters and flow velocities but without MBs. All the peak temperatures initially increased with increasing flow velocities of MBs, followed by a decrease of the peak temperatures with increasing flow velocities when the velocity was higher than the inflection velocity. Meanwhile, cavitation showed a trend of increases with increasing flow velocity. The inflection velocity and cavitation increased with increasing acoustic power and MBs concentration. Thermal lesion appeared around the vessel as MBs flow through the vessel, at which lesion was not observed originally without MBs. These results suggested that this may provide an effective way to minimize thermal losses from perfusion during focused ultrasound exposures.

Blood vessel deformations on microsecond time scales by ultrasonic cavitation

Transient interactions among ultrasound, microbubbles, and microvessels were studied using high-speed photomicrography. We observed liquid jets, vessel distention (motion outward against the surrounding tissue), and vessel invagination (motion inward toward the lumen). Contrary to current paradigms, liquid jets were directed away from the nearest vessel wall and invagination exceeded distention. These observations provide insight into the mechanics of bubble-vessel interactions, which appear to depend qualitatively upon the mechanical properties of biological tissues.

The natural frequencies of microbubble oscillation in elastic vessels

A theoretical model for the dynamics of a bubble in an elastic blood vessel is applied to study numerically the effect of confinement on the free oscillations of a bubble. The vessel wall deformations are described using a lumped-parameter membrane-type model, which is coupled to the Navier-Stokes equations for the fluid motion inside the vessel. It is shown that the bubble oscillations in a finite-length vessel are characterized by a spectrum of frequencies, with distinguishable high-frequency and low-frequency modes. The frequency of the high-frequency mode increases with the vessel elastic modulus and, for a thin-wall vessel, can be higher than the natural frequency of bubble oscillations in an unconfined liquid. In the limiting case of an infinitely stiff vessel wall, the frequency of the low-frequency mode approaches the well-known solution for a bubble confined in a rigid vessel. In order to interpret the results, a simple two-degree-of-freedom model is applied. The results suggest that in order to maximize deposition of acoustic energy, a bubble confined in a long elastic vessel has to be excited at frequencies higher than the natural frequency of the equivalent unconfined bubble.